A Logic for Vagueness

  • John Slaney Australian National University


This paper presents F, substructural logic designed to treat vagueness. Weaker than Lukasiewicz’s infinitely valued logic, it is presented first in a natural deduction system, then given a Kripke semantics in the manner of Routley and Meyer's ternary relational semantics for R and related systems, but in this case, the points are motivated as degrees to which the truth could be stretched. Soundness and completeness are proved, not only for the propositional system, but also for its extension with first-order quantifiers. The first-order models allow not only objects with vague properties, but also objects whose very existence is a matter of degree.


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Author Biography

John Slaney, Australian National University
How to Cite
SLANEY, John. A Logic for Vagueness. The Australasian Journal of Logic, [S.l.], v. 8, nov. 2010. ISSN 1448-5052. Available at: <https://ojs.victoria.ac.nz/ajl/article/view/1815>. Date accessed: 02 july 2020. doi: https://doi.org/10.26686/ajl.v8i0.1815.